Question

Consider the following sequence:

BBB GG BBB GG BB G BB GGG BB G BBBB GGGGG BB

With a 0.05 significance level, we wish to test the claim that the above sequence was produced in a random manner. Answer each of the following questions

(a) The null hypothesis H0H0 is given by

A. The data are in a random order
B. ρ=0ρ=0
C. G=0G=0
D. The data are in an order that is not random
E. n1=n2n1=n2
F. β=0β=0
G. Median=0=0
H. r=0r=0
I. None of the above.

(b) The null hypothesis H1H1 is given by

A. β≠0β≠0
B. Median ≠0≠0
C. n1≠n2n1≠n2
D. ρ≠0ρ≠0
E. G≠0G≠0
F. The data are in an order that is not random
G. The data are in a random order
H. r≠0r≠0
I. None of the above.

(c) The number of runs GG is

A. 1414
B. 2424
C. 1818
D. 3434
E. 3232
F. 1313
G. None of the above.

(d) What kind of test should you conduct

A. Goodness of fit test
B. Runs test for randomness and the test statistic is GG
C. Sign test
D. Runs test for randomness and the test statisc is a zz-score
E. Both sign and goodness of fit tests
F. Independence Test
G. None of the above.

(e) What is/are the critical(s) value(s)

A. The only critical value is -1.96
B. The only critical value is 23
C. The only critical value is 1.96
D. The negative one is -1.96 and the positive one is 1.96
E. The smallest one is -1.96 and the largest one is 1.96  
F. The smallest one is 10 and the largest one is 23
G. The only critical value is 10
H. None of the above.

(f) The conclusion:

A. We reject H0H0 and then there isn't enough evidence to reject the calim that the above sequence was in a random order
B. We reject H0H0 and then there isn't enough evidence to support the calim that the above sequence was in a random order
C. We fail to reject H0H0 and then there isn't enough evidence to reject the calim that the above sequence was in a random order.
D. We reject H0H0 and then there is enough evidence to reject the calim that the above sequence was in a random order
E. We fail to reject H0H0 and then there isn't enough evidence to support the calim that the above sequence was in a random order
F. We fail to reject H0H0 and then there is enough evidence to reject the calim that the above sequence was in a random order
G. We reject H0H0 and then there is enough evidence to support the calim that the above sequence was in a random order
H. We fail to reject H0H0 and then there is enough evidence to support the calim that the above sequence was in a random order
I. None of the above.

Answer 1